The long term objective is to contribute to the solution of many outstanding public problems which involve probability and/or mathematical statistics. Several concrete examples follow. (i) Metastasis. The problem is to estimate the rates at which primary tumors shed metastasis producing cells, taking into account the differences in the growth rate of tumors. (ii) Cell transformation. It is intended to study models of progressive transformations of initiated cells. (iii) Non-identifiability of chance mechanisms operating in survival experiments. As is now known, even the serial sacrifice methodology of Arthur C. Upton is affected by non-identifiability. It is intended to study possibilities to remedy this situation by broading the observational base, e.g., mutagenicity of Bruce Ames. (iv) Screening chemicals for carcinogenicity. The very difficult problem consists of designing an experiment to screen simultaneously several chemicals combined with a methodology of evluation that insures a preassigned low overall frequency of error. (v) Epidemiological studies. Epidemiological studies have many statistical pitfalls. It is intended to review the published reports on such studies and if the occasion arises, to participate in them actively. One particular pitfall stems from the fact that the human populations studied are exposed to a multiplicity of noxious agents, while the whole study is motivated by interest in only a few, perhaps just one, low level of radiation, etc. If it happens that a really important noxious agent is not covered by an epidemiological study, then its effect will be attributed to other agents, perhaps quite innocent. A recent review pointed out that a substantial epidemiological study ended with an absurdity: the filling of air with dust of copper will reduce deaths from cancer of the breast and cancer of the lung. (vi) Sources of problems to be studied. As in the past, problems to be studied will be those inspired by the contemporary public health related literature and by presentations at the Statistical Laboratory seminars.